Maximum distance separable (MDS) array codes are widely employed in the modern
distributed storage systems because they provide the maximum data reliability for a
given level of storage overhead. An \((n,k,m)\)  MDS array code encodes \(km\) 
data symbols into \(nm\)  coded symbols that are equally stored in \(n\)  nodes,
where each node stores \(m\)  symbols. We call the number of symbols stored in each node
as the sub-packetization level. The \((n,k,m)\)  MDS array codes satisfy the MDS property
that is any \(k\)  out of \(n\)  nodes can retrieve all \(km\)  data symbols. The codes are referred
to as systematic codes if the \(km\)  data symbols are included in the first \(k\)  nodes
of obtained \(n\)  nodes. Reed-Solomon (RS) codes [1]} are typical MDS array codes
with \(m = 1\) . In this paper, we consider systematic
MDS array codes that contain \(k\)  data nodes which store the \(km\)  data symbols
and \(r=n-k\)  parity nodes which store the \(rm\)  parity symbols.
